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A178484 For n=1,2,... list all numbers not occurring earlier which can be written as a product of the first n primes raised to some nonnegative power less than n.

%I A178484 #12 May 04 2019 09:45:37
%S A178484 1,2,3,6,4,5,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,
%T A178484 300,450,900,7,8,14,21,24,27,28,35,40,42,49,54,56,63,70,72,84,98,105,
%U A178484 108,120,125,126,135,140,147,168,175,189,196,200,210,216,245,250,252
%N A178484 For n=1,2,... list all numbers not occurring earlier which can be written as a product of the first n primes raised to some nonnegative power less than n.
%C A178484 A condensed version of sequence A178483.
%C A178484 Every positive integer occurs exactly once in this sequence, but depending on its largest prime factor, it may appear later than much larger numbers. E.g. 7=a(29) appears after a(28)=900, and 11=a(257) appears only after a(256)=9261000.
%C A178484 The first n^n terms are the divisors of n#^(n-1), so any term divisible by the k-th prime must appear later than position (k-1)^(k-1). - _Charlie Neder_, Mar 08 2019
%H A178484 Ivan Neretin, <a href="/A178484/b178484.txt">Table of n, a(n) for n = 1..10000</a>
%e A178484 n=1 gives a(1) = 1: numbers 2^a with a < 1.
%e A178484 n=2 gives a(2..4) = [2, 3, 6]: numbers 2^a 3^b with a,b < 2.
%e A178484 n=3 gives a(5..28) = [4, 5, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900]: numbers 2^a 3^b 5^c not occurring earlier, with a,b,c < 3.
%t A178484 DeleteDuplicates@Flatten@Table[Sort[Times @@ (Prime@Range@n^PadLeft[ IntegerDigits[#, n], n]) & /@ (Range[n^n] - 1)], {n, 2, 4}] (* _Ivan Neretin_, May 02 2019 *)
%o A178484 (PARI) { s=0; for( L=1,4, a=[]; forvec( v=vector(L,i,[0,L-1]), bittest(s,t=prod( j=1,L,prime(j)^v[L-j+1] )) & next; s+=1<<t; a=concat(a,t)); print1(vecsort(a)","))}
%Y A178484 Cf. A178480, A178483, A111791.
%K A178484 nonn
%O A178484 1,2
%A A178484 _M. F. Hasler_, May 31 2010